Many carriers have been designed for transporting a bicycle on the back of a motor vehicle. For example, U.S. Pat. No. 4,830,250, issued May 16, 1989 to Newbold et al., describes an adjustable carrier having a pair of U-shaped frame members and a pair of straight support arms, each of which can be adjusted to virtually any angle so as to fit virtually any vehicle. The top tube of the bicycle frame rests on top of the pair of support arms, between a pair of spacer brackets which position the bicycle along the support arm, and beneath an elastic tie cord. The brackets and tie cord together hold the bicycle to the carrier. While the spacer brackets can be moved along the support arms to adjust their position, such adjustment requires the use of a screwdriver which may be inconvenient. Also, the manner in which the brackets engage the top tube of the bicycle frame may not prevent the bicycle from swaying on the carrier and thus knocking against other bicycles on the carrier or the vehicle itself.